High School Calculus Math Course Outline

1.0 Credit

This course includes a thorough study of differentiation and integration with many applications. Limits and continuity are investigated in-depth. The course will emphasize the importance of mathematics studied to date. After completion of this course, the student may wish to take the Advanced Placement Test.

1- Introduction & Review

Welcome to Calculus
Course Outline
Course Syllabus
Completing Math Assessments
Calculus On The Web
Review — Stuff You Should Already Know
Pretest
Assignment: Calculus Pretest

2- Limits & Continuity

An Introduction to Limits & Continuity
Quiz: Introduction to Limits & Continuity
Tangent Lines & Rates of Change
Handout: Tangent Lines & Rates of Change Worksheet
Assignment: Tangent Lines & Rates of Change
The Limit
Handout: The Limit Worksheet
Assignment: The Limit
One-Sided Limits
Handout: One-Sided Limits Worksheet
Assignment: One-Sided Limits
Computing Limits
Handout: Computing Limits Worksheet
Assignment: Computing Limits
Infinite Limits
Handout: Infinite Limits Worksheet
Assignment: Infinite Limits
Limits at Infinity
Handout: Limits at Infinity Worksheet
Assignment: Limits at Infinity
Continuity
Handout: Continuity Worksheet
Assignment: Continuity
Additional Resources
Handout: Limits & Continuity Exam
Assignment: Limits & Continuity Exam

3- Derivatives

Introduction to Derivatives
Definition & Interpretation of the Derivative
Handout: Definition & Interpretation of the Derivative Worksheet
Assignment: Definition & Interpretation of the Derivative
Differentiation Formulas
Handout: Differentiation Formulas Worksheet
Assignment: Differentiation Formulas
Product & Quotient Rule
Handout: Product & Quotient Rule Worksheet
Assignment: Product & Quotient Rule
Derivatives of Trig Functions
Handout: Derivatives of Trig Functions Worksheet
Assignment: Derivatives of Trig Functions
Derivatives of Exponential & Logarithm Functions
Handout: Derivatives of Exponential & Logarithm Functions Worksheet
Assignment: Derivatives of Exponential & Logarithm Functions
The Chain Rule
Handout: The Chain Rule Worksheet
Assignment: The Chain Rule
Implicit Differentiation
Handout: Implicit Differentiation Worksheet
Assignment: Implicit Differentiation
Related Rates
Handout: Related Rates Worksheet
Assignment: Related Rates
Higher Order Derivatives
Handout: Higher Order Derivatives Worksheet
Assignment: Higher Order Derivatives
Additional Resources
Handout: Derivatives Exam
Assignment: Derivatives Exam

4- Applications of Derivatives

What’s the Big Deal About Derivatives, Anyway?
Rates of Change
Critical Points & Extrema
Handout: Critical Points & Extrema Worksheet
Assignment: Critical Points & Extrema
The Shape of a Graph
Handout: The Shape of a Graph Worksheet
Assignment: The Shape of a Graph
The Mean Value Theorem
Handout: The Mean Value Theorem Worksheet
Assignment: The Mean Value Theorem
Optimization
Handout: Optimization Worksheet
Assignment: Optimization
Linear Approximations
Handout: Linear Approximations Worksheet
Assignment: Linear Approximations
Midtest
Assignment: Calculus Midtest
Handout: Applications of Derivatives
Assignment: Applications of Derivatives

5- Integrals

Working Backwards
Indefinite Integrals
Handout: Indefinite Integrals Worksheet
Assignment: Indefinite Integrals
Computing Indefinite Integrals
Handout: Computing Indefinite Integrals Worksheet
Assignment: Computing Indefinite Integrals
Substitution Rule for Indefinite Integrals
Handout: Substitution Rule Worksheet
Assignment: Substitution Rule
Area Problem
Handout: Area Problem Worksheet
Assignment: Area Problem
Definite Integrals
Handout: Definite Integrals Worksheetv
Assignment: Definite Integrals
Computing Definite Integrals
Handout: Computing Definite Integrals Worksheet
Assignment: Computing Definite Integrals
Substitution Rule for Definite Integrals
Handout: Substitution Rule for Definite Integrals Worksheet
Assignment: Substitution Rule for Definite Integrals
Integration by Parts
Handout: Integration by Parts Worksheet
Assignment: Integration by Parts
Partial Fractions
Handout: Partial Fractions Worksheet
Assignment: Partial Fractions
Improper Integrals
Handout: Improper Integrals Worksheet
Assignment: Improper Integrals
Additional Resources
Handout: Integrals Exam
Assignment: Integrals

6- Applications of Integrals

What’s the Big Deal About Integrals, Anyway?
Area Between Curves
Handout: Area Between Curves Worksheet
Assignment: Area Between Curves
Volumes of Solids of Revolution (Part 1)
Handout: Method of Rings Worksheet
Assignment: Method of Rings
Volumes of Solids of Revolution (Part 2)
Handout: Method of Cylinders Worksheet
Assignment: Method of Cylinders
Volume
Work
Handout: Work Worksheet
Assignment: Work
Assignment: Applications of Integrals

7- Sequences & Series

Sequences & Series
Sequences
Series: The Basics
Series: Convergence & Divergence
Special Series
Integral Test
Comparison Test
Alternating Series Test
Absolute Convergence
Ratio & Root Tests
Strategy for Series
Estimating the Value of a Series
Power Series
Taylor Series
Additional Resources
Post-Test
Assignment: Sequences & Series

8- Course Survey

Handout: Course Survey
Assignment: Course Survey

Forest Trail Academy Accreditation and Memberships

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